US 7570049 B2 Abstract A method for estimating a value of a diffusion tensor includes obtaining, from a plurality of test subjects, DT-MRI data from which an initial estimate of the tensor can be derived. Values indicative of intra-subject variation and inter-subject variation in the data are then determined. These values are used to determine a subject-specific additive offset for adjusting the DT-MRI data.
Claims(10) 1. A computer-implemented method for estimating the evolution of a diffusion tensor using DT-MRI data provided by an MRI system, the method comprising:
obtaining, from each of a plurality of test subjects, DT-MRI data representing a time series of diffusion tensors associated with each test subject;
using a computer to reduce the DT-MRI data to determine individual data descriptive of the evolution of tensor values for each of the test subjects;
causing a computer to reduce the individual data to determine data descriptive of the evolution of a diffusion tensor associated with the plurality of test subjects; and
outputting the data descriptive of the evolution of a diffusion tensor associated with the plurality of test subjects.
2. The computer-implemented method of
determining a plurality of individual mean functions, each of which corresponds to a test subject; and
determining a plurality of individual covariance matrices, each of which corresponds to a test subject.
3. The computer-implemented method of
4. The computer-implemented method of
5. The computer-implemented method of
6. A computer-readable medium having encoded thereon software for estimating the evolution of a diffusion tensor using DT-MRI data provided by an MRI system, the software comprising computer-executable instructions for:
obtaining, from each of a plurality of test subjects, DT-MRI data representing a time series of diffusion tensors associated with each test subject;
reducing the DT-MRI data to determine individual data descriptive of the evolution of tensor values for each of the test subjects;
reducing the individual data to determine data descriptive of the evolution of a diffusion tensor associated with the plurality of test subjects.
7. The computer-readable medium of
determining a plurality of individual mean functions, each of which corresponds to a test subject; and
determining a plurality of individual covariance matrices, each of which corresponds to a test subject.
8. The computer-readable medium of
9. The computer-readable medium of
10. The computer-readable medium of
Description This application is a US national stage under 35 U.S.C. §371 of PCT/US2005/011280 filed Apr. 6, 2005, which is a continuation-in-part of U.S. Ser. No. 10/823,816 filed Apr. 14, 2004 now U.S. Pat. No. 7,268,551. These applications are herein incorporated by reference. The disclosure relates to brain tractography, and in particular, to estimating a diffusion tensor field in brain tissue using data from multiple subjects. The brain includes gray matter connected by channels of white matter, sometimes referred to as fiber bundles, or fasciculi. A purpose of tractography is to identify the paths followed by the white matter, to use those paths to form a normative map of a fully functional brain, and to detect differences between functional and dysfunctional brains. A physiological characteristic of the white matter tracks is that water will tend to diffuse anisotropically in the direction of those tracks. Thus, by observing the directions in which water diffuses at different locations in the brain, one can identify the directions of major fiber bundles within the brain tissue. The preferred direction of diffusion, and the extent of that preference, can be described by a tensor field made up of diffusion tensors with each diffusion tensor being associated with a different location in the brain. Thus, if one could evaluate the diffusion tensor at each point in the brain tissue, one would be able to determine the directions of the fiber bundles in that tissue. One technique of tractography is to use diffusion tensor magnetic resonance imaging (“DT-MRI”) to observe the diffusion of water in brain tissue. Using those observations, one can infer the value of the diffusion tensor at different locations in that tissue. To reduce the likelihood that anomalies in a single subject will skew the resulting measurements, imaging is carried out on a large number of subjects. Data obtained from the subjects is then averaged across all subjects. In principle, this technique will average out differences between subjects. One difficulty with this approach is that it is almost impossible to ensure that the brains of two different subjects are perfectly aligned during the MRI data collection period. In fact, even if one were to take two measurements of the same subject, one might obtain two different results, simply because the location of the subject's head in the MRI machine may not be identical for both measurements. Thus, variation between measurements can arise from several causes. First, variations may arise from the anatomical differences between patients. These are among the variations that are to be averaged out. However, variations may also arise from poor “registration” (i.e. alignment of images) between subjects. These variations have no anatomical significance and will therefore tend to corrupt any estimate of the diffusion tensor. Additional sources of variation having no anatomical significance include machine noise (for example, eddy currents, RF noise, or noise in the hardware) and physiological noise (for example, artifacts, cardiac pulsation, and magnetic susceptibility). These noise sources add to variation across subjects. The invention provides a system and method for processing DT-MRI data to substantially remove the effect of unmeasured and unspecified variations when estimating values of an aggregate diffusion tensor over multiple subjects. In one aspect, the invention includes a method for estimating a value of a diffusion tensor by obtaining, from a plurality of test subjects, DT-MRI data from which an initial estimate of the tensor can be derived. First and second values, indicative of intra-subject and inter-subject variation in the data respectively, are then determined. At least in part on the basis of the first and second values, a subject-specific additive offset is then determined for adjusting the DT-MRI data. One practice of the invention further includes generating adjusted data by adjusting the DT-MRI data by the offset. Another practice of the invention includes generating a bowtie plot from the adjusted data. The DT-MRI data can represent an initial estimate of the diffusion tensor value. Alternatively, the DT-MRI data can represent echo data from which an initial estimate of the diffusion tensor can be derived. Additional practices of the invention include those in which determining a first value includes determining an average intra-subject variance and those in which determining a second value includes determining an inter-subject variance. In another aspect, the invention includes a computer-readable medium having encoded thereon software for estimating a value of a diffusion tensor. The software includes instructions for obtaining, from a plurality of test subjects, DT-MRI data from which an initial estimate of the tensor can be derived; determining first and second values indicative of intra-subject variation and inter-subject variation in the data respectively; and, at least in part on the basis of the first and second values, determining a subject-specific additive offset for adjusting the DT-MRI data. In some embodiments, the software includes instructions for generating adjusted data by adjusting the DT-MRI data by the offset. In other embodiments, the software includes instructions for generating a bowtie plot from the adjusted data. In yet other embodiments, the software includes instructions for selecting the DT-MRI data to represent an initial estimate of the diffusion tensor value. Alternatively, the software includes instructions for selecting the DT-MRI data to represent echo data from which an initial estimate of the diffusion tensor can be derived. Additional embodiments of the invention include those in which the software includes instructions for determining a first value by determining an average intra-subject variance and software that includes instructions for determining a second value by determining an inter-subject variance. Another aspect of the invention includes a system for estimating a value of a diffusion tensor. The system includes an MRI machine; a processor in data communication with the MRI machine; and a computer-readable medium in data communication with the processor. The computer-readable medium has encoded thereon software having instructions for obtaining, from a plurality of test subjects, DT-MRI data from which an initial estimate of the tensor can be derived; determining first and second values indicative of intra-subject variation and inter-subject variation in the data respectively; and, at least in part on the basis of the first and second values, determining a subject-specific additive offset for adjusting the DT-MRI data. The invention also includes a method for estimating the evolution of a diffusion tensor by obtaining, from each of a plurality of test subjects, DT-MRI representing a time series of diffusion tensors associated with each test subject; reducing the DT-MRI data to determine individual data descriptive of the evolution of tensor values for each of the test subjects; and reducing the individual data to determine data descriptive of the evolution of a diffusion tensor associated with the plurality of test subjects. In some practices of the invention, reducing the individual data includes determining a plurality of individual mean functions, each of which corresponds to a test subject; and determining a plurality of individual covariance matrices, each of which corresponds to a test subject. In other practices of the invention, reducing at least one of the collective data and the individual data comprises determining a growth model. Exemplary growth models include, but are not limited to, parametric growth-models, semi-parametric growth-models, and non-parametric growth-models. Other practices include those in which reducing at least one of the collective data and the individual data includes determining a longitudinal model. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although methods similar or equivalent to those described herein can be used in the practice or testing of the present invention, suitable methods are described below. All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. In case of conflict, the present specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting. Other features and advantages of the invention will be apparent from the following claims, the detailed description, and the accompanying figures. The tensor field within a volume of brain tissue is characterized by a 3×3 diffusion tensor associated with each voxel within the tissue: Tractography typically includes estimating the values the diffusion tensors that make up the diffusion tensor field. The resulting estimate can be used to determine the orientation of white matter tracks in the brain. One way to estimate the values of the diffusion tensors is to obtain magnetic resonance images of several subjects and to combine data from those images to obtain canonical diffusion tensors descriptive of a “standard” brain. Because of variations associated with experimental measurements, both within a particular subject and between subjects, it is often necessary to perform certain statistical processing steps to obtain a meaningful estimates of the canonical diffusion tensors. One way to perform the statistical processing is to aggregate all the measurements from all the subjects at each voxel and to obtain an average of those measurements, at each voxel. As an example, In fact, this is clearly not the case. The subjects are not clones of each other. They are separate individuals that are anatomically and physiologically different from each other. In addition, it is virtually impossible to place the subjects into an MRI machine in such a way that the brains of each subject are at the same location relative to the MRI machine. To make matters worse, the physiological “noise” associated with each subject will differ from that associated with other subjects. For example, one subject may be apprehensive about being confined in an MRI machine and may therefore have a higher heart rate than the other subjects. Or, a particular subject may become apprehensive over time, thereby causing the physiological noise to be non-stationary during the course of a measurement. These and other data-corrupting influences remain unaccounted for in the method shown in Referring to Since there are six non-redundant elements, there will ultimately be six such matrices associated with the first subject. However, as the method is carried out separately for each of the six non-redundant tensor elements, it is useful to consider in detail the processing associated with only one v×v matrix, shown as D As indicated in The initial diffusion tensor estimates D Referring to Referring back to The index e for indexing the data vector and data matrix is intended to index a particular one of the six non-redundant tensor elements over the voxel field. As shown by the while loop in Referring now to The next step is to obtain an average of the intra-subject variances corresponding to each subject (step The next step is to obtain an estimate of the inter-subject variance (step The next step is to obtain a vector of subject-specific offsets. This vector is a weighted version of the residual error vector r Next, the diffusion tensor estimate D As described herein, the method is carried out on the initial estimates of the diffusion tensor elements. However, the same method can be applied to the MRI echo data used to generate the estimates of the diffusion tensor elements for each subject, thereby providing improved estimates of D The particular steps described herein provide a convenient method, using linear-algebraic operators, for manipulating data arranged as described in connection with The foregoing method provides a way to obtain a canonical multi-subject diffusion tensor that represents a standard brain at a single point in time. One can then use an observed deviation between this canonical diffusion tensor and that of a particular brain to assess the condition of that particular brain. The process of obtaining the canonical diffusion tensor includes obtaining, from each of several subjects, a snapshot of that subject's brain at a particular time. There are, however, conditions, particularly developmental conditions, that are not readily observed by comparing the difference between a canonical diffusion tensor and the diffusion tensor of a particular brain. In many cases, these conditions only become apparent when comparing the evolution of a particular diffusion tensor with the evolution of the canonical diffusion tensor. To obtain data representing the evolution of the canonical diffusion tensor, it becomes necessary to obtain, for each of several subjects, a sequence of diffusion tensor-MRI images of that subject's brain. As an example of the distinction between observing the diffusion tensor and observing the evolution of a diffusion tensor, The regression lines for the three subjects each have different slopes and intercepts. Yet, it is apparent from The method described herein identifies a canonical evolutionary trend in the diffusion tensor elements at multiple locations in the brain. In this way, the method makes it possible to compare the evolutionary trend of a particular brain with that of a standard brain. On the basis of this comparison, it is possible to identify developmental disorders that might otherwise remain hidden. Referring now to Similarly, time series of echo data {S The individual mean functions The individual change-maps The individual and collective data-reduction models can be identical. However, they need not be. Either or both data-reduction models can be implemented as any growth-curve or other model. One common growth-curve model is a classical exponential growth model, for example of the form
The individual covariance matrices Referring to DT-MRI data was obtained from twelve healthy male volunteers as described in Following correction of distortion from eddy currents, the diffusion tensor was estimated for each voxel in each subject using linear regression techniques described in The DT-MRI volume from each subject was elastically normalized to a standard anatomical reference space, using the MNI EPI template supplied as part of SPM (The Wellcome Department of Cognitive Neurology, Institute of Neurology, London, UK), by employing a procedure similar to that outlined in Once each subject's tensor volume had been estimated, the principal eigenvector, which was the eigenvector associated with the largest eigenvalue, was determined in each voxel and its 2-D projection onto the plane was represented by a small bar of unit length. The orientation plots thus obtained from each of the twelve subjects were then overlaid. This visualization method is termed a ‘bow-tie plot’ due to its appearance at those voxels in which the principal eigenvectors from the twelve subjects are modestly well aligned. In The invention can be implemented in hardware or software, or a combination of both. The invention can be implemented in computer programs using standard programming techniques following the method steps and figures described herein. The programs should be designed to execute on programmable computers each comprising a processor, a data storage system (including memory and/or storage elements), at least one input device, and at least one output device, such as a CRT or printer. Program code is applied to input data to perform the functions described herein and generate output information. The output information is applied to one or more output devices such as a CRT, as described herein. Each program is preferably implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the programs can be implemented in assembly or machine language, if desired. In any case, the language can be a compiled or interpreted language. Each such computer program is preferably stored on a storage medium or device (e.g., ROM or magnetic diskette) readable by a general or special purpose programmable computer, for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. The system can also be considered to be implemented as a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner to perform the functions described herein. It is to be understood that while the invention has been described in conjunction with the detailed description thereof, the foregoing description is intended to illustrate and not limit the scope of the invention, which is defined by the scope of the appended claims. Other aspects, advantages, and modifications are within the scope of the following claims. Patent Citations
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